Turbulent resistivity in wavy two-dimensional magnetohydrodynamic turbulence

Journal of Fluid Mechanics

Volumn 595, Issue , 2008, Pages 173-202

  Keating, Shane R ^a   Diamond, P H ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BUOYANCY; CORIOLIS FORCE; ELECTRIC CONDUCTIVITY; KINETICS; REYNOLDS NUMBER; TURBULENT FLOW;

MAGNETIC POTENTIAL; TURBULENT RESISITIVITY; WAVE-INTERACTION-DRIVEN FLUX;

MAGNETOHYDRODYNAMICS;

BUOYANCY; CORIOLIS FORCE; ELECTRIC CONDUCTIVITY; KINETICS; MAGNETOHYDRODYNAMICS; REYNOLDS NUMBER; TURBULENT FLOW;

CORIOLIS FORCE; EDDY; ELECTRODYNAMICS; KINETICS; MAGNETOHYDRODYNAMICS; REYNOLDS NUMBER; THEORETICAL STUDY; TURBULENCE; TWO-DIMENSIONAL FLOW;

EID: 38049180887     PISSN: 00221120     EISSN: 14697645     Source Type: Journal    
DOI: 10.1017/S002211200700941X     Document Type: Article

References (47)

1. BENNEY, D. J. & NEWELL, A. C. 1969 Random wave closures. Stud. Appl. Maths 48, 29.
2. BLACKMAN, E. G. & FIELD, G. B. 2000 Constraints on the magnitude of α in dynamo theory. Astrophys. J. 534, 984-988.
3. BLACKMAN, E. G. & FIELD, G. B. 2002 New dynamical mean-field dynamo theory and closure approach. Phys. Rev. Lett. 89, 265007.
4. BRACCO, A., PROVENZALE, A., SPIEGEL, E. A. & YECKO, P. 1998 Spotted discs. In Theory of Black Hole Accretion Disks (ed. M. A. Abramowicz, G. Bjornsson & J. E. Pringle), pp. 254-270.
5. CATTANEO, F. 1994 On the effects of a weak magnetic field on turbulent transport. Astrophys. J. 434, 200-205.
6. CATTANEO, F. & VAǏNSHTEǏN, S. I. 1991 Suppression of turbulent transport by a weak magnetic field. Astrophys. J. 376 L21-L24.
7. DAVIDSON, R. C. 1972 Methods in Nonlinear Plasma Theory. Academic.
8. DIAMOND, P. H., ITOH, S.-I., ITOH, K. & HAHM, T. S. 2005 Zonal flows in plasmas - a review. Plasma Phys. Control. Fusion 47 R35-R161.
9. DIAMOND, P. H., ITOH, S.-I., ITOH, K. & SILVERS, L. 2007 β-plane magnetohydrodynamic turbulence and dissipation in the solar tachocline. In Proc. of the Tachocline Dynamics Workshop (Nov. 2004, Isaac Newton Institute, Cambridge, UK) (ed. D. W. Hughes, R. Rosner & N. O. Weiss). Cambridge University Press.
10. FYFE, D. & MONTGOMERY, D. 1976 High-beta turbulence in two-dimensional magnetohydrodynamics. J. Plasma Phys. 16, 181-191.
11. FYFE, D., MONTGOMERY, D. & JOYCE, G. 1977 Dissipative, forced turbulence in two-dimensional magnetohydrodynamics. J. Plasma Phys. 17, 369-398.
12. GALTIER, S., NAZARENKO, S. V., NEWELL, A. C. & POUQUET, A. 2000 A weak turbulence theory for incompressible magnetohydrodynamics. J. Plasma Phys. 63, 447-488.
13. GRUZINOV, A. V. & DIAMOND, P. H. 1994 Self-consistent theory of mean-field elctrodynamics. Phys. Rev. Lett. 72, 1651-1653.
14. GRUZINOV, A. V. & DIAMOND, P. H. 1996 Nonlinear mean-field elctrodynamics of turbulent dynamos. Phys. Plasmas 3 (5), 1853-1857.
15. HASSELMANN, K. 1966 Feynmann diagrams and interaction rules of wave-wave scattering processes. Rev. Geophys. 4, 1-32.
16. KABURAKI, O. & UCHIDA, Y. 1971 Magnetohydrodynamic wave-mode coupling. Quantum field-theoretical approach to weakly non-linear case with application to solar coronal heating. Publ. Astr. Soc. Japan 23, 405.
17. KLEEORIN, N. I. & RUZMAIKIN, A. A. 1982 Dynamics of the average turbulent helicity in a magnetic field. Magnetohydrodynamics 19 116-122, transl. from Magnitaya Gidrodinamika.
18. KLEEORIN, N. I., ROGACHEVSKII, I. V. & RUZMAIKIN, A. A. 1990 Magnetic force reversal and instability in a plasma with advanced magnetohydrodynamic turbulence. Sov. Phys. J. Exp. Theor. Phys. 70, 878.
19. KROMMES, J. A. 2002 Fundamental statistical descriptions of plamsa turbulence in magnetic fields. Phys. Rep. 360, 1-352.
20. KULSRUD, R. M. & ANDERSON, S. W. 1992 The spectrum of random magnetic fields in the mean field dynamo theory of the galactic magnetic field. Astrophys. J. 396, 606-630.
21. MCCOMAS, C. H. & BRETHERTON, F. P. 1977 Resonant interaction of oceanic internal waves. J. Geophys. Res. 82, 1397-1412.
22. MIESCH, M. S. 2005 Large-scale dynamics of the convection zone and tachocline. Living Rev. Solar Phys. 2, 1.
23. MIKHAILOVSKII, A. B., NOVAKOVSKAIA, E. A., LAKHIN, V. P., NOVAKOVSKII, S. V. & ONISHCHENKO, O. G. 1989 A contribution to the theory of weakly turbulent Kolmogorov spectra of a homogeneous magnetized plasma. Sov. Phys., J. Exp. Theor. Phys. 95, 1598-1613.
24. MOFFATT, H. K. 1970 Dynamo action associated with random inertial waves in a rotating conducting fluid. J. Fluid Mech. 44, 705-719.
25. MOFFATT, H. K. 1972 An approach to a dynamic theory of dynamo action in a rotating conduting fluid. J. Fluid Mech. 53, 385-399.
26. MOFFATT, H. K. 1978 Magnetic Field Generation in Electrically Conducting Fluids. Cambridge University Press.
27. NG, C. S. & BHATTACHARJEE, A. 1997 Scaling of anisotropic spectra due to the weak interaction of shear-Alfvén wave packets. Phys. Plasmas 4, 605-610.
28. OZMIDOV, R. V. 1965 On the turbulent exchange in a stably stratified ocean. Izv. Acad. Sci. USSR, Atmos. Ocean. Phys. 1 853-860.
29. PEIERLS, R. E. 1929 Zur kinetischen theorie der wärmeleitungen in kristallen. Ann. Phys. 3, 1055-1101.
30. PHILLIPS, O. M. 1960 On the dynamics of unsteady gravity waves of finite amplitude. Part 1. J. Fluid Mech. 9, 193-217.
31. POUQUET, A. 1978 On two-dimensional magnetohydrodynamic turbulence. J. Fluid Mech. 88, 1-16.
32. POUQUET, A., FRISCH, U. & LEORAT, J. 1976 Strong magnetohydrodynamic helical turbulence and the nonlinear dynamo effect. J. Fluid Mech. 77, 321-354.
33. RHINES, P. B. 1975 Waves and turbulence on a β-plane. J. Fluid Mech. 69, 417-443.
34. SAGDEEV, R. Z. & GALEEV, A. A. 1969 Nonlinear Plasma Theory. W. A. Benjamin.
35. SILVERS, L. J. 2005 Dynamic effects of a magnetic field on diffusion in a chaotic flow. Phys. Lett. A 334, 400-405.
36. SILVERS, L. J., KEATING, S. R. & DIAMOND, P. H. 2008 On cross-phase and the quenching of the turbulent diffusion of magnetic fields in two dimensions. Astrophys. J. Lett. (submitted).
37. SPIEGEL, E. A. & ZAHN, J.-P. 1992 The solar tachocline. Astron. Astrophys. 265, 106-114.
38. STAQUET, C. & SOMMERIA, J. 2002 Internal gravity waves: From instabilities to turbulence. Annu. Rev. Fluid Mech. 34, 559-593.
39. STEENBECK, M., KRAUSE, F. & RÄDLER, K. H. 1966 A calculation of the mean electromotive force in an electrically conducting fluid in turbulent motion under the influence of coriolis forces. Z. Naturf. A 21, 369-376.
40. TING, A. C., MONTGOMERY, D. & MATTHAEUS, W. H. 1986 Turbulent relaxation processes in magnetohydrodynamics. Phys. Fluids 29 3261-3274.
41. TOBIAS, S. M. 2005 The solar tachocline: Formation, stability and its role in the solar dynamo. In Fluid Dynamics and Dynamos in Astrophysics and Geophysics (ed. A. M. Soward, C. A. Jones, D. W. Hughes & N. O. Weiss), pp. 193-234. CRC Press.
42. TSINOBER, A. B. 1975 Magnetohydrodynamic turbulence. Magnitnaia Gidrodinamika 1, 7-22.
43. VAǏNSHTEǏN, S. I. & ZEL'DOVICH, Y. B. 1972 Origin of magnetic fields in astrophysics. Sov. Phys. Usp. 15, 159.
44. WERSINGER, J. M., FINN, J. M. & OTT, E. 1980 Bifurcation and 'strange' behavior in instability saturation by nonlinear three-wave coupling. Phys. Fluids 23 (6), 1142-1154.
45. ZAKHAROV, V. E., L'VOV, V. X. & FALKOVICH, G. 1992 Kolmogorov Spectra of Turbulence I. Springer.
46. ZEL'DOVICH, YA. B. 1957 The magnetic field in the two-dimensional motion of a conducting turbulent liquid. Sov. Phys. J. Exp. Theor. Phys. 4, 460-462.
47. ZEL'DOVICH, YA. B., RUZMAIKIN, A. A. & SOKOLOFF, D. D. 1983 Magnetic Fields in Astrophysics. Gordon & Breach.